What do I do?
If you've known this a girl a long time I doubt that it will make things too awkward if you ask her to homecoming. She might really like to go with you. Next time you are talking to her just say "Hey, do you have a date for Homecoming yet?" and if she says no, then ask "Would you like to go with me?" If she says no you could just say "Oh, that's too bad. I was hoping that we could go as friends" or whatever. That way, you aren't really losing any face.
If you realize that things have started to become awkward between the two of you, tell her that you really like having her as a friend and hope that it didn't make her feel awkward by you asking her to Homecoming. And tell her that you'd like things to be the way they were before and that you value her friendship.
Good luck, and I hope you have a great time at Homecoming.